The OP songs for One Piece have some great memories attached to them for me, so those would be my initial picks. I also like the OP song for Magic Knights Rayearth and Lodoss War: Chronicles of the Heroic Knight. For something more recent, I'd go with Attack on Titan's OP (who wouldn't? )

If the music is fitting for the theme and atmosphere of the work, then I'll probably react to it accordingly. To me, music can be an incredibly powerful emotional medium. I can lose myself in an artistic creation so much easier if said creation can be juxtaposed with music. (or you know...already is music)

Inuyasha's soundtrack is quite nostalgic for me--especially the songs by Do As Infinity

Spice and Wolf's opening themes are just amazing and set the tone of the show very nicely.

Attack on Titan's OP/ED themes were quite effective as well. The second closing theme is just an all around great song though.

The OP for Guilty Crown, it gets me riled up emotionally. Not sad, or teary, or anything. It's just kind of uplifting and touching.
The OP for Nodame Cantabile: Paris, that song makes me happy every time I hear it. I had to go download it.